Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32894 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#32897 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×2−1+6 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
3512 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 71 points:
(1,2,3,4,5,6,7)(8,9,15,21)(10,22,26,43)(11,27,30,45)(12,18,32,42)(13,20,14,19)(16,33,38,25)(17,35,40,29)(23,36,51,62)(24,52,55,47)(28,57,60,64)(31,44,34,41)(37,54,63,53)(39,58,65,59)(46,49,56,50)(48,67,69,61)(66,68,71,70);(8,10)(9,16)(11,23)(12,24)(13,33)(14,25)(15,26)(17,36)(18,37)(19,43)(20,22)(21,38)(27,56)(28,48)(29,50)(30,51)(31,54)(32,55)(34,53)(35,49)(39,61)(40,62)(41,47)(42,63)(44,52)(45,46)(57,71)(58,70)(59,68)(60,69)(64,66)(65,67);(8,11,15,30)(9,17,21,40)(10,23,26,51)(12,28,32,60)(13,29,14,35)(16,36,38,62)(18,39,42,65)(19,27,20,45)(22,46,43,56)(24,48,55,69)(25,49,33,50)(31,58,34,59)(37,61,63,67)(41,64,44,57)(47,66,52,71)(53,68,54,70);(8,12)(9,18)(10,24)(11,28)(13,34)(14,31)(15,32)(16,37)(17,39)(19,44)(20,41)(21,42)(22,47)(23,48)(25,54)(26,55)(27,57)(29,59)(30,60)(33,53)(35,58)(36,61)(38,63)(40,65)(43,52)(45,64)(46,66)(49,70)(50,68)(51,69)(56,71)(62,67)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 25885);